Uncertainty Quantification of Spalart–Allmaras Turbulence Model Coefficients for Compressor Stall

Abstract

The turbulence model in Reynolds-averaged Navier–Stokes simulations is crucial in the prediction of the compressor stall margin. In this paper, parametric uncertainty of the Spalart–Allmaras turbulence model in predicting two-dimensional airfoil stall and three-dimensional compressor stall has been investigated using a metamodel-based Monte Carlo method. The model coefficients are represented by uniform distributions within physically acceptable ranges. The quantities of interest include characteristic curves, stall limit, blockage size, and turbulence magnitude. Results show that the characteristics can be well predicted in the stable flow range, but the inaccuracy and the uncertainty increase when approaching stall. The stall point of the airfoil can be enveloped by the parametric uncertainty range, but that of the rotor cannot. Sensitivity analyses identified the crucial model coefficients to be source related, where an increase in the predicted turbulence level will delay the onset of stall. Such results imply that implementing new turbulence production terms with respect to the rotor-specific flow features is likely to improve the model accuracy. The findings in this paper not only provide engineering rules of thumb for the model users but also guide the future implementation of a data-driven turbulence model for the model developers.